Table of Contents

1. Introduction

Getting Started

What does Regina do?

Triangulations

Census Creation

Normal Surfaces

Angle Structures

Splitting Surfaces

Scripting

Interfaces

Documentation

Data Files

Genealogy

Citing Regina

Who is Regina?

2. Working with Packets

The Packet Tree

Available Packet Types

Container

Text

Triangulation

Normal Surface List

Surface Filter

Angle Structure List

Script

The Packet Tree Menu

Creating New Packets

Cloning

Viewing and Editing

Renaming

Deleting

Refreshing a Subtree

3. Triangulations

Creation

New Triangulations

Imported Triangulations

Census Creation

Analysis

Basic Properties

Face Gluings

Skeletal Information

Algebraic Properties

Combinatorial Composition

Properties of Normal Surfaces

SnapPea Calculations

Census Lookup

Modification

Editing Face Gluings

Elementary Moves

Global Subdivision

Global Simplification

Extensions

0-Efficiency

Double Cover

Crushing Normal Surfaces

Decomposition

Component Decomposition

Connected Sum Decomposition

4. Normal Surfaces

Creation

Analysis

List Properties

Individual Surface Coordinates

Individual Surface Properties

Original Matching Equations

Crushing and Cutting

Crushing a Surface

Cutting Along a Surface

Filtering

Creating Filters

5. Angle Structures

Creation

Analysis

List Properties

Individual Angle Structures

Individual Structure Properties

6. Importing and Exporting Data

Importing

Regina Data File

SnapPea Triangulation

Orb / Casson Triangulation

Dehydrated Triangulation List

Python Script

Exporting

Regina Data File

Regina Data File (Uncompressed)

SnapPea Triangulation

C++ Source

CSV Surface List

Python Script

7. Python Scripting

Scripting Overview

Invoking Scripting

Using Python

Documentation

Caveats

Cooperating with the GUI

Ownership Concerns

International Characters

Sample Python Sessions

Working with a triangulation

Working with a packet tree

Reporting progress of long operations

8. Configuration

General Options

Triangulation Options

Normal Surface Options

Census Options

Python Options

Python Libraries

SnapPea Options

9. Using Regina in Other Code

Installing the Development Files

Other Required Software

Compiler and Linker Flags

10. Troubleshooting and FAQ

11. Bug Tracking and Mailing Lists

12. License and Acknowledgements

License Details

Citation

Copying and Modification

SnapPea Kernel

Orb Kernel

Acknowledgements

I. Main Applications

regina-kde - Regina KDE user interface

regina-python - Regina command-line Python interface

II. Specialised Utilities

regconcat - Combine several Regina data files

regconvert - Convert between different Regina file formats

regfiledump - Dump the contents of a Regina data file

regfiletype - Identify the formats of Regina data files

sigcensus - Form a census of splitting surface signatures

tricensus - Form a census of 3-manifold triangulations

tricensus-manager - Distribute a triangulation census amongst several machines

tricensus-mpi - Distribute a triangulation census amongst several machines using MPI

tricensus-mpi-status - Summarise the log file of an MPI census of triangulations

trisetcmp - Compare triangulations between two Regina data files

III. Data File Format

abeliangroup - An abelian group

allowstrict - Does an angle structure list span a strict structure?

allowtaut - Does an angle structure list span a taut structure?

cancrush - Can a normal surface be safely crushed?

compact (filter) - A constraint on compactness

compact (surface) - Is a normal surface compact?

connected - Is a normal surface connected?

euler (filter) - A constraint on Euler characteristic

euler (surface) - The Euler characteristic of a normal surface

filter - A normal surface filter

filter (combination) - A logical combination surface filter

filter (properties) - A surface filter that uses basic properties

flags - An arbitrary set of flags

fundgroup - The fundamental group of a triangulation

group - A group presentation

H1 - The first homology group of a triangulation

H1Bdry - The first homology group of the boundary of a triangulation

H1Rel - The relative first homology group of a triangulation

H2 - The second homology group of a triangulation

line - A single line of text

op - A single logical operation

orbl (filter) - A constraint on orientability

orbl (surface) - Is a normal surface orientable?

packet - A single packet in a data file

packet (angle structure list) - An angle structure list packet

packet (container) - A container packet

packet (normal surface list) - A normal surface list packet

packet (script) - A script packet

packet (surface filter) - A surface filter packet

packet (text) - A text packet

packet (triangulation) - A triangulation packet

params - Parameters for a normal surface enumeration

realbdry (filter) - A constraint on real boundary

realbdry (surface) - Does a normal surface have real boundary?

reginadata - An entire Regina data file

reln - A relation in a group presentation

splitsfce - Does a triangulation have a splitting surface?

struct - A single angle structure

surface - A single normal surface

tag - An individual packet tag

tet - A single tetrahedron in a triangulation

tetrahedra - The tetrahedra forming a triangulation

text - An arbitrary amount of text

turaevviro - A single Turaev-Viro invariant for a triangulation

twosided - Is a normal surface two-sided?

var - A single script variable

zeroeff - Is a triangulation 0-efficient?

A. Version History

Bibliography

Index